Field of the Invention
The invention concerns a method for the determination of diffusion gradients for recording diffusion-weighted magnetic resonance image data with anisotropic diffusion directions. The invention also concerns a method for recording diffusion-weighted magnetic resonance image data of an object under examination, diffusion-gradient-determining computer, and a magnetic resonance system.
Description of the Prior Art
As used herein, “magnetic resonance recordings” should be understood to mean image data from the interior of the object under examination generated with the use of a magnetic resonance scanner controlled during the course of the method, as well as parameter maps reflecting a spatial or temporal distribution of specific parameter values inside the object under examination that can be generated from the image data. A “recording” of magnetic resonance image data should be understood to mean the performance of an image-recording method by the operation of a magnetic resonance imaging system.
Diffusion-weighted magnetic resonance recordings are magnetic resonance recordings with which the diffusion movement of specific substances, in particular water molecules, in the body tissue can be scanned and depicted in a spatially resolved manner. Diffusion imaging has proven effective in everyday clinical practice, in particular for the diagnosis of stroke, since the affected regions of the brain can be recognized much earlier in diffusion-weighted images than is possible in conventional magnetic resonance recordings. In addition, diffusion imaging is being increasingly used in the fields of oncologic, cardiologic and musculoskeletal diseases. One variant of diffusion-weighted magnetic resonance tomography is diffusion tensor imaging with which the dependence on direction of the diffusion is detected. As used herein, diffusion-weighted magnetic resonance recordings include both magnetic resonance recordings generated within the context of diffusion-weighted magnetic resonance tomography methods and magnetic resonance recordings generated within the context of diffusion tensor imaging.
For the generation of diffusion-weighted magnetic resonance recordings, it is first necessary to acquire diffusion-encoded raw data. This done using special scanning sequences, hereinafter called diffusion gradient scanning sequences. These scanning sequences are characterized by, after a customary deflection of the spins into a plane perpendicular to the basic magnetic field of the magnetic resonance tomography scanner, the activation of a specific sequence of gradient magnetic field pulses that vary the field strength of the external magnetic field in a prespecified direction. With a diffusion movement, the precessing nuclear spins move out of phase, and thus can be identified in the measuring signal.
During diffusion imaging, usually, a number of images with different diffusion directions and weightings, i.e. with different diffusion-encoding gradient pulses, are recorded and combined with one another. The degree of the diffusion weighting is generally defined by the so-called diffusion weighting factor, also called the “b-value”. The different diffusion images or the images or parameter maps combined therefrom can then be used for the desired diagnostic purposes. In order to be able to assess the influence of the diffusion movement correctly, in many cases a further reference recording in which no diffusion-encoding gradient pulse is activated, i.e. an image with b=0, is used for comparison. The pulse scanning sequence for the acquisition of the reference raw data is structured similarly to the diffusion gradient scanning sequence with the exception of the emission of the diffusion-encoding gradient pulses. Alternatively, it is also possible to perform a reference recording with a b-value ≠0.
For diagnosis, with MR-diffusion imaging, usually images or parameter maps are used with which a free diffusion process is assumed, which is also called a free normal Gaussian diffusion process that has an apparent diffusion coefficient (ADC). This process is characterized by, in dependence on the diffusion-weighting factor, the signal strength drops in accordance with an exponential relationship.
Extensions of this model take account of, for example, the dependence on direction of the diffusion in microscopically limited geometries. For example, water molecules can move along nerve fibers more quickly than perpendicular thereto. The diffusion-tensor model also acquires these relationships under the assumption of a free normal Gaussian diffusion process, which is now direction-independent, and permits the calculation and depiction of associated parameters or parameter values, such as parameters relating to the directional anisotropy.
There is also a series of further approaches with which deviations from Gaussian behavior can be described with corresponding model functions. These include, for example the IVIM model (IVIM=intra-voxel incoherent motion) with which it is assumed there is bi-exponential drop in the signal amplitude in dependence on the b-value due to perfusion effects. This class of approaches also includes the Kurtosis model with which deviations from the exponential dependence of the signal strength are modeled from the b-value with higher-order tensors.
The acquisition of a number of diffusion directions and/or weightings enables a more precise image of the local diffusion geometry to be obtained. In this way, HARDI (high angular resolution diffusion imaging), DSI (diffusion spectrum imaging) or Q-Ball methods (see David S. Tuch, “Q-Ball Imaging”, Magnetic Resonance in Medicine 52:1358-1372 (2004)) enable a number of preferred directions to be resolved with an image voxel.
There are also methods with which the dependence of the signal intensity is taken account of experimentally not only by the b-value and the direction, but also by specific interval durations in order to use model assumptions to draw conclusions relating to microscopic tissue parameters (for example the axon radius, the surface-to-volume ratios etc.).
The last mentioned group of methods offers the possibility of generating new diffusion-based contrasts possibly with a high clinical value.
When recording diffusion data by diffusion-weighted magnetic resonance imaging, the available gradient amplitude G represents a central performance feature. This is because the greater the gradient amplitude, the shorter the time required to implement a prespecified diffusion weighting. This can be identified from the Stejskal-Tanner equation:b=γ2G2τ2(Δ−τ/3).  (1)
Here, γ is the gyromagnetic ratio, τ is the duration of each of the other two (ideally assumed to be rectangular) diffusion gradients and Δ is the temporal spacing of the diffusion gradients. If, for example, the gradient G is doubled, under the assumption that the gradient duration τ remains unchanged, the effective duration T=Δ−τ/3 can be reduced to a quarter if the b-value is to remain the same. The term “a quarter” applies approximately if the value of the temporal spacing of the diffusion gradients Δ is high compared to the value of the gradient duration τ. FIG. 1 illustrates a Stejskal-Tanner sequence for diffusion-weighted magnetic resonance imaging.
Therefore, the gradient amplitude G has a direct influence on the achievable signal-to-noise ratio (SNR) of an individual scan. This is because, with a shortened diffusion encoding time, it is possible to reduce relaxation influences, for example by a reduction in the echo time which is then possible. The SNR gain can, for example, be used to improve image quality, to reduce scanning time or increase resolution.
In order to make optimum use of the maximum gradient amplitude of a system available for each physical axis available, pulses usually are applied to several axes simultaneously. In this context, the decisive factor for the diffusion encoding is the vector sum of the amplitude of the effective gradient Geff=√{square root over (Gx2+Gy2+Gz2,)} which can be up to √{square root over (3)} higher than the amplitudes of the individual axes Gx, Gy, Gz.
During an isotropic diffusion process with which no direction is indicated, in principle, scanning with one diffusion direction is sufficient. In this case, it is possible to select the gradient amplitudes Gx=Gy=Gz=Gmax and obtain Geff=Gmax*√{square root over (3)} as the effective gradient, i.e. the maximal possible performance. However, in tissue types with pronounced anisotropies, such as, for example, nerve or muscle fibers, this approach produces undefined results, since the diffusion weighting is dependent upon the a priori unknown relative alignment between the tissue and the gradients' coordinate system.
In addition, during the determination of specific diffusion coefficients, such as, for example, trace-weighting, derived diffusion coefficients ADC or tensor variables, such as, for example, fractional anisotropy, diffusion-weighted image recordings with several diffusion directions are required for which defined boundary conditions have to be satisfied. As a rule, the additional boundary conditions significantly limit the possibilities for simultaneous application to several axes.
For the quantification of an anisotropic diffusion process, for example in the form of a trace coefficient, the recording of at least three non-collinear diffusion directions is required. Suitable direction sets are, for example:
orthogonal: (Gx, Gy, Gz)=(1, 0, 0), (0, 1, 0), (0, 1, 0),
with this direction set: Geff=Gmax;
optimized orthogonal: (Gx, Gy, Gz)=(1, 1, −1/2), (1, −1/2, 1), (−1/2, 1, 1),
with this direction set:
            G      eff        =                  G        max            *                        9          4                      ;
tetrahedral: (Gx, Gy, Gz)=(−1, 1, 1), (1, −1, 1), (−1, −1, −1), (1, 1, −1),
with this direction set: Geff=Gmax*√{square root over (3)};
octahedral: (Gx, Gy, Gz)=(1, 0, 1), (−1, 0, 1), (0, 1, 1), (0, 1, −1), (0, 1, −1), (1, 1, 0), (−1, 1, 0),
with this direction set: Geff=Gmax*√{square root over (2)}.
Although the tetrahedral direction set has the maximum performance, it is not possible to determine tensor data with this set.
The octahedral direction set can be used to determine tensor data because it contains six non-collinear directions, distributed isotropically in space. This simultaneously entails the conventional tensor-suitable direction set with the highest known effective gradient amplitude Geff.
The direction sets known in the prior art with a larger number of directions all have smaller effective amplitudes, which, in borderline cases of a very high number of directions, lead to an isotropic distribution of a unit sphere with an effective amplitude Geff=Gmax.